Constant-volume transition entropy

Kato, T., Phase transition behaviors of a main chain liquid crystal and elucidation of constant-volume transition entropy [in Japanese], Master s thesis, Tokyo Institute of Technology, 2002. 

The present examples have provided a useful test for the validity of the hypothetical process adopted conventionally for the estimation of the constant-volume transition entropy. Although the estimation of the yu value using the relation y = a/ rmder ordinary pressure (method 1) is simple, the process should not be excluded because of its simplicity unless a more prevailing form of y(V) is known. 

Estimation of Constant-Volume Transition Entropies at the NI and CN Interphase... 

As comparison of Tables 2 and 4 indicates, the changes in volume and entropy at the NI transition obtained for the mainchain dimer and trimer liquid crystals are much larger than those reported for conventional monomer liquid crystals [112]. In Tables 2 and 3, the constant-volume transition entropies (AStr)v are expressed in terms of joules per mole per kelvin. The conformational entropy changes estimated on the basis of the NMR quadrupolar splitting data observed in the LC state are as follows = 13.3... 

For MBBE-6, the ytr values are also available from method 2 (Sect. 3.2.1). As mentioned in the preceding section, the difference between methods 1 and 2 is quite small except for kcn(N). An increment of 25% in ycN(N) gives rise to a decrease in ( AScn)v by approximately 20% from those listed in colunm 7 of Table 3. As shown in Tables 2 and 3, the experimental values of the latent entropy (AStr)p (column 6) are quite divergent depending on the method PVT or DIA) employed in the measurement. This is also a source of the uncertainties in the final estimates of the constant-volume transition entropy (AStr)v (column 7). 

Constant-volume transition entropy RIS/ H NMR analysis Segmented LC... 

Comparison with the Constant-Volume Transition Entropy. 117... 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

The standard entropy difference between the reactant(s) of a reaction and the activated complex of the transition state, at the same temperature and pressure. Entropy of activation is symbolized by either A5 or and is equal to (A// - AG )IT where A// is the enthalpy of activation, AG is the Gibbs free energy of activation, and T is the absolute temperature (provided that all rate constants other than first-order are expressed in temperature-independent concentration units such as molarity). Technically, this quantity is the entropy of activation at constant pressure, and from this value, the entropy of activation at constant volume can be deduced. See Transition-State Theory (Thermodynamics) Gibbs Free Energy of Activation Enthalpy of Activation Volume of Activation Entropy and Enthalpy of Activation (Enzymatic)... 

The transition at 19° C involves an expansion of 0.0058 cm3/g (Clark and Muus). Sincethe transition temperatureincreaseswith pressure by about 0.013° C per atmosphere (Beecroft and Swenson), the latent heat is about 3.2 cal/g. These values are for the crystal and would be reduced in proportion to the crystalline content. The transition at 30° C is only about one-tenth as large. The over-all increase in entropy at these transitions is about 0.0108 cal deg-1g-1. The portion due to the increase in volume is (a// ) A V, where a is the volumetric coefficient of thermal expansion and / is the compressibility. Since the compressibility of the crystal is not known, this quantity is somewhat uncertain. Using the average of the values of a (Quinn, Roberts, and Work) and p (Weir, 1951) for the whole polymer above and below the transitions, it appears that (a/P)A V is about 0.0041 cal deg 1g 1. The entropy of the transition corrected to constant volume is, therefore, about 0.0067 cal deg g-1. 

Abe, A., and Nam, S. Y, PVT smdies on dimer liquid crystals and estimation of transition entropies at constant volume. Macromolecules, 28, 90-95 (1995). 

Orwoll, R. A., Sullivan, V. J., and Campbell, G. C., Thermal pressure coefficients and specific volumes of cyanobiphenyls and their transition entropies at constant volume. Mol. Cryst. Liq. Cryst., 149, 121-140 (1987). 

The slope of the phase boundary curve dpidt can be estimated from the Ttr - Pit plot obtained by using a PVT or high-pressure differential thermal analysis (DTA) method [118,119]. The volume-dependent entropy (correction for the volume change) ASy, the transition entropy (AStr)p under ordinary pressure, and the constant-volume entropy (AStr)v obtained therefrom are arranged in this order in Tables 2,3, and 4. 

The second-order nature of the transition is confirmed since the entropy change at the transition is zero. This can be shown by calculating the entropy density (at constant volume), s ... 

In the above-mentioned RIS/ H NMR analysis, the volume change inevitable to the first-order phase transition is not taken into account. The mainchain LCs normally exhibit stepwise phase transitions with temperature. In most cases, the volume change takes place about 10% at the NI and 90% at the CN transition [32]. In order to confirm the validity of conformational transition entropies, pressure-volume-temperature (PVT) measurements were performed for the ether analogs CBA-9 and CBA-10 to determine the NI entropy change at constant volume ( A5ni)v ... 

There are actually a variety of polymer properties that change at the glass transition (modulus, specific volume, enthalpy, entropy, specific heat, refractive index, and dielectric constants), a variety of physical methods to measure the glass transition and, indeed, a variety of ways to define glass transition (5,21). 

Figure 2.16 illustrates schematically how the free energy, entropy, and heat capacity of a closed, constant volume system are related for first-order phase transitions where both phases coexist at the transition temperature, Tp. Each... 

The entropy change AS/ - and the volume change AV/ - are the changes which occur when a unit amount of a pure chemical species is transferred from phase I to phase v at constant temperature and pressure. Integration of Eq. (4-18) for this change yields the latent heat of phase transition ... 

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